"The Concept of State"

From: Judith Rosen <***>

Date: Wed, 26 May 2004 20:40:01 -0400

From "Life, Itself", page 69, in the chapter called "The Concept of
State", under the sub-heading 4B: "Chronicles":

Robert Rosen wrote:

"I will begin by stepping back a bit, by supposing that we do
not yet have a notion of state at our disposal. In effect, I will retreat to the
level of percepts and perceptions and treat the self as a pure observer. The
idea of state, being a concept and not a percept, thus does not yet enter the
picture at all. Thus, all we have is the self looking out at its ambience. What
does it see?

All the self can see is a sequence of percepts,
ordered by its subjective sense of time. We suppose that the self can choose
which percepts it will look at (in more sophisticated language, which
variables it will measure) and whether it will look continuously or sample at
discrete intervals. (Subjective) time is itself a complicated concept (see AS),
but it is a primitive that we can take for granted at this level. Thus, the
result of the self looking at its ambience is only a tabulation; a list of what
is seen, indexed by when it is seen. Such a list we shall call a
chronicle.

Chronicles can thus be completely arbitrary things, at least
insofar as what is tabulated in them is concerned. Weather bureaus,
stock exchanges, census takers, and a host of other familiar institutions
provide endless streams of them. In the scientific realm, they are
data. To the historian, entirely concerned with what happened when,
they are the very stuff of existence.

To the (applied) mathematician, and to the statistician, a
chronicle is simply a time series. It is thus a way of associating
events, or attributes of events, with numbers (instants of time). It is even an
effective way of associating events with numbers; all we need to do is
wait for the appropriate instant to occur and then tabulate the corresponding
event. In formal terms, then, a chronicle or time series is simply a
mapping from numbers to events or their attributes; for simplicity, we
can even suppose it to be a completely formal mapping from numbers to
numbers.

But the self is not merely an observer. Doubtless the self has
heard of Natural Law, and hence, does not believe in sequences of events that
are entirely arbitrary. Further, the self may be impatient and unwilling to wait
for the unfolding of time to reveal events to come; it would like to extend its
chronicle into the future before the sequence of events does so for it.
Likewise, in addition to being impatient, it may be curious about what its time
series was like before the self actually started looking at it or tabulating
it.

So, along with any time series (which we shall think of
henceforth as a piece of a mapping from numbers to numbers) comes the urge to
extend it into the future and into the past, to extrapolate it, to predict and
to post-dict.

The most elementary thing we can do in these directions is
attempt extrapolation on the basis of the fragment at our disposal, our data. At
this level, we do not know or care what the individual entries in our tabulation
mean; we try to use the data as the basis for extrapolation into the
future or into the past. This is, of course, itself a very syntactic approach;
it presupposes that what we need inheres somehow in the very structure of the
list or chronicle itself, apart from all other considerations and all other
chronicles. Put another way, we seek to extract from the structure of the list
itself something that will already entail those entries that are yet to
come or those that have come before.

Thus, for instance, if the self is a statistician, it will
look for correlations which it may or may not find; but in any case, all it
can find this way are properties of the list, and not in
general of what the list represents. Clearly, Natural Law does not operate at
this level. It is not a law that in general favors statisticians, though this
has not inhibited their activities.

[A good one-liner there, Dad!]

Indeed, the enterprise of trying to find the operation of
Natural Law from the contemplation of arbitrary chronicles or lists of data is
precisely the dilemma of experimental science itself. At root, of course, the
problem is one of induction, which I have already briefly discussed above (see
section 2K); it is a problem of extrapolating from a sample of a universe to the
entire universe from which the sample was drawn. In the present case, we are
sampling in too many ways; we are obviously sampling over an extremely limited
time frame, but we are also sampling what we do observe and tabulate from the
universe of what we could observe and tabulate. As always, these sampling
processes corrupt us in two ways; they loseinformation precisely
because they are samples, and they also add irrelevant information
(noise), which pertains to the sampling process
itself.

As we have seen, the problem of induction is generally
hopeless, because arbitrary properties, simply by virtue of being arbitrary, do
not reveal themselves in samples. Stated otherwise, no sample entails
anything about a non-sampled instance. Hence, the problem of extrapolating
arbitrary time series is likewise hopeless.

There are two strategies we can adopt to cope with this
hopeless situation. The first of these is to retain the idea of sampling but
simply sample more and different attributes. Each of these will, of course, just
give us other, a new time series, more data. The hope here is that multiple
series will do what one alone generally cannot, namely, entail, on the
basis of the internal structure of the set of chronicles, what
unsampled entries must be (and especially, of course, particularly those entries
that are yet unsampled) [future
samples].

The other strategy is to be more judicious in the attributes
we are sampling. Although the arbitrary induction problem is hopeless, there are
those properties that do admit sampling and extrapolation. As we saw earlier,
these are properties for which entailment already exists between the
entries in the sample or chronicle.

The concept of state embodies both of these
strategies; more chronicles, more judiciously chosen. We will consider what is
involved in the subsequent sections."

[The next section, 4C, entitled "Recursive Chronicles", has a lot of
mathematical illustration, but the final paragraph, which is all prose, sums up
what he was illustrating quite well...]:

"In general, whenever we isolate something, either in the
ambience or in the internal world of the self, and ask "why?" about it, we are
treating it as an effect and inquiring about its causes. One way to cope with
such questions is precisely to produce a recursive chronicle, a
history, which starts from some convenient initial condition and takes
us to the effect we inquired about, through a chain of successive entailments
(i.e., a trajectory) arising from a mapping and its iterates. In the circle of
ideas we are in the process of developing [that
describes what contemporary physics "believes"], which
will culminate in the concept of state, causality manifests itself
only through a sequence of state transitions, entailing an effect that
is again a state. Although, as we shall see, a number of important tactical
details intervene, this is the basic picture that permeates all of contemporary
science. If there is something wrong with the picture, or especially if there is
something missing from it, then the root of the trouble lies already
here."